Parameters \(x_1\)  and \(x_2\)  are the
horizon of each driver, in the sense
that a driver situated at \(x\)  adjusts his speed
according to the average vehicular density he
sees on interval
\([x-x_1,x+x_2]\) . We followed the exact same
numerical approximation of the convolution
integral presented in [1]}. And
we selected two situations (as in
[1]}): (1) the drivers
look forward or (2) backward \((x_1,x_2) = (0,0.25)\) 
and \((x_1,x_2) = (0.25,0).\)  The initial condition is given by
\(\rho _{0}(x) = {\left\lbrace \begin{array}{ll}\frac{1}{2}, \text{ for } -2.8 \le x \le -1.8; \quad \quad \frac{3}{4}, \text{ for } -1.2 \le x \le -0.2; \\\frac{3}{4}, \text{ for } 0.6 \le x \le 1.0;\quad 1, \text{ for } 1.5 \le x < \infty ; \quad 0, \text{ otherwise.}\end{array}\right.}\) 
